Reconstruction of directional sources using physics-informed neural networks

In the context of augmented/virtual reality applications, replicating the directivity of sound sources is a critical step to ensure a high-quality immersive experience. However, accurate directivity measurements require complex experimental procedures involving a high number of microphones. In these scenarios, spatial interpolation allows to reconstruct the sound field with fewer sensors, which can be sparsely distributed around the source. The literature offers several interpolation schemes for sound field reconstruction, although they exhibit limited accuracy due to the lack of knowledge on the underlying physics. Recently, Physics-Informed Neural Networks (PINN) have been used to directly solve partial differential equations and thus better predict the evolution of dynamical systems. In this manuscript, we propose a spatial interpolation scheme based on PINN for the reconstruction of sound source directivity. PINN are used to solve the Helmholtz equation starting from acquisitions of the directivity over a limited set of sparsely distributed points. Results are compared with the outcomes of well-established methods based on Spherical Harmonics Decomposition (SH), Thin Plate Pseudo-Splines Interpolation (SPLI) and Piece-wise Linear Spherical Triangular Interpolation (TRI). PINN prove to provide better reconstruction of the directivity with respect to the proposed comparison methods, even when dealing with highly sparse sampling grids.